Polar Complex Exponential Transform Research Articles

Topological Analysis of Image Reconstruction Based on Polar Complex Exponential Transform

Image moments are an important tool used for image reconstruction. An image can be represented in terms of image moments, which is known as image reconstruction from its moments. To construct an image from the moments, a question often arises that how many moments are required for the reconstruction of image. Theoretically, many image moments may be required for accurately reconstructing an image. However, since image moment construction can be computationally challenging, often in practice only a finite number of moments are used for the image reconstruction. The difference in reconstructed and original image for many numbers of images can lead to a satisfying answer. However, accurate reconstruction may not often be possible, and we are often relying on other approaches to find similarity between the original image and reconstructed image. We used a similarity based on a topological data analysis tool known as the persistence diagram, determining the bottleneck distance between the original and the reconstructed image as the measure of similarity. Our investigation was conducted on the common images utilized in image processing tasks. The findings indicate that there is no direct correlation between the number of moments and the quality of image reconstruction. It is necessary to choose an appropriate number of moments, which may be very small, instead of calculating a high number of image moments.

Improved polar complex exponential transform for robust local image description

Image description via robust local descriptors plays a vital role in a large number of image representation and matching applications. In this paper, we propose a novel distinctive local image descriptor that is based on the phase and amplitude information of Polar Complex Exponential Transform (PCET). The proposed descriptor, called IPCET (Improved PCET), is robust to the common photometric transformations (e.g., illumination, noise, JPEG compression, and blur) and geometric transformations (e.g., scaling, rotation, translation, and significant affine distortion). We perform extensive experiments to compare our IPCET descriptor with six most cutting-edge region descriptors (i.e., SIFT, Zernike Moment, GLOH, PCA-SIFT, SURF, and ORB). Experimental results demonstrate that our IPCET descriptor outperforms cutting-edge moment-based descriptors.

Double Medical Images Zero-Watermarking Algorithm Based on the Chaotic System and Ternary Accurate Polar Complex Exponential Transform

Double Medical Images Zero-Watermarking Algorithm Based on the Chaotic System and Ternary Accurate Polar Complex Exponential Transform

A robust video zero-watermarking based on deep convolutional neural network and self-organizing map in polar complex exponential transform domain

In this paper, a robust video zero-watermarking scheme for copyright protection using a combination of convolutional neural network (CNN) and self-organizing map (SOM) in polar complex exponential transform (PCET) space is presented. The scheme is developed not only to remedy the existing problems of lacking in some performance assessments but also to enhance the robustness. It starts with extracting the content feature of each frame by CNN and then some significant frames are selected using SOM clustering and maximum entropy. Secondly, the PCET is applied to all selected frames to abstract invariant moments, and further, is scrambled by a chaotic logistic map and is reduced in dimensions by singular value decomposition (SVD). Next, a binary sequence is generated by comparing adjacent values of the obtained compact PCET moments in the previous step, and further is permuted to produce a binary matrix. Finally, a bitwise exclusive-OR operation is imposed on the binary matrix and the encrypted watermark by the chaotic map to generate a zero-watermark signal. Experimental results demonstrate that the proposed scheme has adequate equalization and distinguishability of zero-watermarks as well as strong robustness against common signal processing, geometric, compression, and inter-frame attacks. Also, compared with existing video zero-watermarking and traditional video watermarking methods, the proposed scheme exhibits superior robustness.

Robust and accurate detection of image copy-move forgery using PCET-SVD and histogram of block similarity measures

Many block-based detection methods for image copy-move forgery have been reported. However, their performance degrades significantly under different geometric attacks such as rotation and scaling. In this paper, we propose a novel robust and accurate detection scheme for image copy-move forgery. It mainly consists of three steps: firstly, a suspicious image is divided into overlapping circular blocks, and polar complex exponential transform (PCET) is employed to extract geometric invariant feature of each block. Next, singular value decomposition (SVD) is applied to the coefficient matrix composed of extracted geometric invariant moments for dimension reduction. Meanwhile, the histogram of block similarity measures is adopted to estimate the optimal similarity threshold. Finally, the calculated similarity threshold is used for block matching process and consequently more accurate tampered areas are obtained. Experimental results on various datasets show that the proposed image copy-move detection approach outperforms other existing methods in the aspect of resisting geometric rotation and scaling attacks, with the adaptability of similarity threshold and low computational complexity.

GPU Accelerated Polar Harmonic Transforms for Feature Extraction in ITS Applications

Polar Harmonic Transform (PHT) is termed to represent a set of transforms those kernels are basic waves and harmonic in nature, which can improve the effect in Intelligent Transportation System (ITS) applications. PHTs consist of Polar Complex Exponential Transform (PCET), Polar Cosine Transform (PCT) and Polar Sine Transform (PST). PHTs can extract orthogonal and rotation invariant features and demonstrated superior performance in various image processing and computer vision applications. For real time systems and large multimedia databases, execution efficiency is always a significant challenge. With widespread use of Graphics Processing Unit (GPU), this study presents GPU based PHTs. Proposed methods are based on mathematical properties of PHTs and optimization techniques of GPU. Optimal parameter selections for GPU execution are also discussed. In our experiments, proposed methods are over 1800 times faster.

Color image zero-watermarking based on fast quaternion generic polar complex exponential transform

As one promising solution, zero-watermarking techniques have been proposed to enhance the image visual quality and applied to protect the intellectual property rights of the medical images, remote sensing images and military images. Owing to their favorable image description capability and geometric invariance, moments and moment invariants have become a popular tool for the zero-watermarking. However, two issues of the moments-based zero-watermarking methods should be addressed: First, most of them ignore the analysis and experiment on discriminability, resulting in a high false positive ratio; Second, direct computation of the moments from their definition is inefficient, numerically unstable and inaccurate, which severely affects the performances of these moments-based methods. To overcome the two challenges, in this paper, we present a Fast Quaternion Generic Polar Complex Exponential Transform (FQGPCET) based color image zero-watermarking algorithm. We first propose a novel computation strategy, i.e. FGPCET, to solve the moments computing problems. We then show that it is possible to generate a robust and discriminative image feature, by mixing the low-order QGPCET moments/coefficients. And finally, we develop a new color image zero-watermarking approach using FQGPCET and asymmetric tent map. Theoretical analysis and experimental results show that the proposed zero-watermarking algorithm achieves a good trade-off between robustness and discriminability, and has certain superiority in terms of security, capacity and time complexity.

An Image Copy-Move Forgery Detection Method Based on SURF and PCET

With the maturity of image editing software, image content has been forged frequently, posing potential threats to many critical fields. To detect forgery images effectively, this paper proposes an image copy-move forgery detection (CMFD) method based on speeded-up robust feature (SURF) and polar complex exponential transform (PCET). Firstly, image is divided into non-overlapping irregular image blocks by superpixel segmentation. Then, these image blocks are separated into two categories: smooth regions and texture regions. Secondly, after finding the keypoints by SURF, the PCET coefficients are extracted and utilized for searching similar features by feature matching algorithm. Thirdly, a strategy is used to eliminate false matched points and find the regions with dense matched points. It combines the random sample consensus (RANSAC) algorithm and a filtering scheme. Finally, mathematical morphology and an iterative strategy are adopted to refine the tampered regions. Compared with other CMFD methods, the proposed method can detect the forgery which occurs in high-brightness smooth regions or forgery images involving similar but genuine regions. Experimental results also indicate the proposed method can resist different distortions by various attacks, including rotation, scaling, blurring, joint photographic expert group (JPEG) compression, and noise addition.

Parallel Multi-Core CPU and GPU for Fast and Robust Medical Image Watermarking

Securing medical images are a very essential process in medical image authentication. Medical image watermarking is a very popular tool to achieve this goal. In this paper, an extremely fast, highly accurate, and robust algorithm is proposed for watermarking both gray-level and color medical images. In the proposed method, a scrambled binary watermark is embedded in the host medical image. Simplified exact kernels are used to compute the moments of the polar complex exponential transform (PCET) for the host gray-level images and the moments of the quaternion PCET for the host color images without approximation errors. The stability of the computed moments enables us to use higher order moments in a perfect reconstruction of the watermarked medical images. The accurate moment invariant to rotation, scaling, and translation ensures the robustness of the proposed watermarking algorithm against geometric attacks. Performed experiments clearly show very high visual imperceptibility and robustness to different levels of geometric distortions and common signal processing attacks. The implementation of parallel multi-core CPU and GPU result in a tremendous reduction of the overall watermarking times. For a color image of size $256\times256$ , the watermarking time is accelerated by $20\times $ and $11\times $ using a GPU and a CPU with 16 cores, respectively.

Highly accurate and numerically stable higher order QPCET moments for color image representation

A novel method is proposed for highly accurate, fast and numerically stable computation of the higher order Quaternion Polar Complex Exponential Transform (QPCET) moments for color images in polar Coordinates. A novel mathematical formula is derived and used to avoid numerical instabilities at higher orders. The proposed method removes the approximation errors involved in conventional methods and provides high image reconstruction capabilities. The proposed method results in a highly accurate rotation invariance. Numerical experiments are performed where the obtained results are compared with those of the recent existing methods.

Multi-granularity geometrically robust video hashing for tampering detection

The wide-spread video editing tools make it much easier to tamper a video, which raises a huge need for authentication techniques that can prove the originality of video content and locate the tampered regions on the video sequences. In this paper, a multi-granularity geometrically robust video hashing method is proposed for tampering detection and localization. In order to balance the robustness and sensitiveness, we describe a video from three levels of granularity: frame sequence level, block level and pixel level, and then hashes are generated at these three levels. Polar Complex Exponential Transform (PCET) moments are calculated on the low-pass sub-band of 3D Discrete Wavelet Transform (3D–DWT) on frame sequence to extract geometric invariant spatio-temporal hash, which is used for video authentication. Local PCET moments are calculated on annular and angular blocks, which are used for geometric correction and coarse tampering localization. Position information of salient objects is obtained from saliency map for fine tampering localization. Experimental results show that the proposed method is robust against temporal de-synchronization and geometrical transformation, and has high tampering localization accuracy even when the video is rotated. Compared with state-of-the-art methods, it is more robust against content-preserving operations and more sensitive to malicious manipulations.

Copy–move forgery detection based on multi‐radius PCET

Copy–move, which copies part of an image and pastes to another part of the same image, is one of the most commonly used image tampering operations. The copied part may suffer to post-processing operations such as rotation, scaling and blur to make the forgery visually convincing. To detect the copied parts with large-scale rotation and scaling, this study proposes a copy–move forgery detection method based on multi-radius polar complex exponential transform (PCET). First, the multi-radius PCET with graphic processing unit acceleration is used to extract the rotational invariant and multi-scale features. Then, the lexicographical order matching algorithm, optimised with minimum heap is applied to get a coarse match result. After that, the accurate detection based on radius ratio and position information is used to get the accurate detection result. Compared with the state-of-the-art methods, the proposed method can detect the copied parts with large-scale rotation or scaling and is robust against Joint Photographic Experts Group (JPEG) compression, smoothing and noise degrading.

Copy Move Forgery Image Detection via Discrete Radon and Polar Complex Exponential Transform-Based Moment Invariant Features

Copy move forgery with geometric distortions such as the rotational operation, the scaling operation, the mirror operation and the additive noise operation became more common. Existing methods are not competent for the detection of the copy move forgery with these distortions. In fact, the most critical issue for the detection of the forgery is the determination of the geometric features. This paper proposes an efficient Discrete Radon Polar Complex Exponential Transform (DRPCET)-based method for the extraction of the rotational and the scaling invariant features for the copy move forgery detection. First, the features obtained by the Radon transform (RT) and the Polar Complex Exponential Transform (PCET) are fused together. Then, these features are normalized. In order to achieve the scaling invariant property, an auxiliary circular template is introduced. With the auxiliary circular template, the translational moment invariant features, the rotational moment invariant features and the scaling moment invariant features are constructed for the extraction of the planar geometrical features. By further extracting some useful features for the representation of the image background, the interference of the background information can be reduced. After extracting the geometrical features, the lexicographic sorting is applied. Then, a correlation between the same part or similar parts of the image which are copied and moved to another image is computed. Based on the obtained correlations, these forgery parts can be identified and their composed positions can be located. Finally, these images are denoted as the forgery image. Extensive computer numerical simulations have been performed. The obtained results show that the proposed method can detect the copy move region in the forgery image precisely even though the forgery regions are suffered from the mixed geometric distortions.

Robust zero-watermarking algorithm based on polar complex exponential transform and logistic mapping

This paper introduces a new zero-watermarking algorithm based on polar complex exponential transform (PCET) and logistic mapping. This algorithm takes advantage of the geometric invariance of PCET to improve the robustness of the algorithm against geometric attacks, and the logistic mapping’s sensitivity to initial values to improve the security of the algorithm. First, the algorithm computes the PCET of the original grayscale image. Then it randomly selects PCET coefficients based on logistic mapping, and computes their magnitudes to obtain a binary feature image. Finally, it performs an exclusive-or operation between the binary feature image and the scrambled logo image to obtain the zero-watermark image. At the stage of copyright verification, the image copyright can be determined by performing the exclusive-or operation between the feature image and the verification image and comparing the resulting image to the original logo image. Experimental results show that this algorithm has excellent robustness against geometric attacks and common image processing attacks and better performance compared to other zero-watermarking algorithms.

Breast Cancer Detection Using PCPCET and ADEWNN: A Geometric Invariant Approach to Medical X-Ray Image Sensors

In the field of radiology, mammographic screened images (i.e. X-ray image sensing) are very challenging and difficult to interpret. The expert radiologist visually hunts the mammograms for any specific abnormality. However, human factor causes a low degree of precision that often results in biopsy and anxiety for the patient involved. This paper proposes a novel computer-aided detection (CAD) system to reduce the human factor involvement and to help the radiologist in automatic diagnosis of malignant/nonmalignant breast tissues by utilizing polar complex exponential transform (PCET) moments as texture descriptors. The input region of interest is extracted manually and subjected to further number of preprocessing stages. Both magnitude and phase of PCET moments are used for feature extraction of suspicious region. Moreover, a new classifier adaptive differential evolution wavelet neural network is introduced to improve the classification accuracy of the proposed CAD system. The proposed system is tested on the mammographic images from Mammographic Image Analysis Society database. The designed system attains a fair accuracy of 97.965% with 98.196% sensitivity and 97.194% specificity. The best area under the receiver operational characteristics curve for the proposed classifier is found to be 0.984 with confidence interval from 0.968 to 0.999 and ±0.0108 standard error.

Research on Copy-Move Image Forgery Detection Using Features of Discrete Polar Complex Exponential Transform

With the aid of sophisticated photo-editing software, such as Photoshop, copy-move image forgery operation has been widely applied and has become a major concern in the field of information security in the modern society. A lot of work on detecting this kind of forgery has gained great achievements, but the detection results of geometrical transformations of copy-move regions are not so satisfactory. In this paper, a new method based on the Polar Complex Exponential Transform is proposed. This method addresses issues in image geometric moment, focusing on constructing rotation invariant moment and extracting features of the rotation invariant moment. In order to reduce rounding errors of the transform from the Polar coordinate system to the Cartesian coordinate system, a new transformation method is presented and discussed in detail at the same time. The new method constructs a [Formula: see text] shrunk template to transform the Cartesian coordinate system back to the Polar coordinate system. It can reduce transform errors to a much greater degree. Forgery detection, such as copy-move image forgery detection, is a difficult procedure, but experiments prove our method is a great improvement in detecting and identifying forgery images affected by the rotated transform.

PCET based copy-move forgery detection in images under geometric transforms

With the advent of the powerful editing software and sophisticated digital cameras, it is now possible to manipulate images. Copy-move is one of the most common methods for image manipulation. Several methods have been proposed to detect and locate the tampered regions, while many methods failed when the copied region undergone some geometric transformations before being pasted, because of the de-synchronization in the searching procedure. This paper presents an efficient technique for detecting the copy-move forgery under geometric transforms. Firstly, the forged image is divided into overlapping circular blocks, and Polar Complex Exponential Transform (PCET) is employed to each block to extract the invariant features, thus, the PCET kernels represent each block. Secondly, the Approximate Nearest Neighbor (ANN) Searching Problem is used for identifying the potential similar blocks by means of locality sensitive hashing (LSH). In order to make the algorithm more robust, morphological operations are applied to remove the wrong similar blocks. Experimental results show that our proposed technique is robust to geometric transformations with low computational complexity.

Discrete Polar Complex Exponential Transform for Image Rotation Duplication Detection

This paper through Comparative analysis of This Discrete Polar Complex Exponential Transform approach is improved from traditional Polar Complex Exponential Transform (PCET) and this transform also encompasses the features of orthogonality and rotation invariance. We introduce a new 9×9 circle instead of a unit circle in DPCET to calculate features of image more precision. And various experiments were performed to prove that effectiveness of our approach in detecting duplicated forgeries, with translation, rotation, noise addition. And the experiment results also show that our approach is more robust to geometric distortions of the duplicated regions than other compared approaches.

Discriminative Moment Feature Descriptors for Face Recognition

Zernike Moment (ZM) is a promising technique to extract invariant features for face recognition. It has been modified in previous studies to Discriminative ZM (DZM), which selects most discriminative features to perform recognition, and shows improved results. The present paper proposes modification of DZM, named Modified DZM (MDZM), which selects coefficients based on their discriminative ability by considering extent of variability between their class-averages. This reduces within-class variations while maintaining between-class differences. The study also investigates this idea of feature selection on recently introduced Polar Complex Exponential Transform (PCET) (named discriminative or DPCET). Performance of the techniques is evaluated on ORL, Yale and FERET databases against pose, illumination, expression and noise variations. Accuracy improves up to 3.1% by MDZM at reduced dimensions over ZM and DZM. DPCET shows 1.9% of further improvement at less computational complexity. Performance is also tested on LFW database and compared with many other state-of-art approaches.

Combined Rotation- and Scale-Invariant Texture Analysis Using Radon-Based Polar Complex Exponential Transform

Polar complex exponential transform (PCET) is superior to pseudo Zernike moment-based method in terms of kernel generation, numerical stability and easier implementation. Their performance degrades under additive noise such as white Gaussian noise. Moreover, these methods show poor performance against directional information of texture. In this paper, a new rotation- and scale-invariant method for texture analysis using Radon transform and PCET for textured image is proposed. Scale and translation invariance is achieved by normalization process in Radon space, and rotation invariance is obtained by combining Radon transform with PCET. A k-nearest neighbor classifier is employed to classify the texture. To test and evaluate the proposed method, several sets of textures were experimented with different scaling, translation and rotation in different noisy conditions. The correct classification percentage is calculated under the varying standard deviation. Experimental results show preeminence of the proposed method as compared to the existing invariant texture analysis methods.